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A124992
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Primes of the form 14k+1 generated recursively. Initial prime is 29. General term is a(n)=Min {p is prime; p divides (R^7 - 1)/(R - 1); Mod[p,7]=1}, where Q is the product of previous terms in the sequence and R = 7Q.
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29, 70326806362093, 43, 127, 59221, 113, 32411, 71, 4957, 74509, 4271, 19013, 239, 2003, 463, 421, 613575503674084673, 32089, 211, 54601, 3109
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All prime divisors of (R^7 - 1)/(R - 1) different from 7 are congruent to 1 modulo 14.
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REFERENCES
| M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.
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LINKS
| N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
| a(3) = 43 is the smallest prime divisor congruent to 1 mod 14
of (R^7 - 1)/(R - 1) =
8466454975669959912248567627122565866080343755024168315838344565727361366925647440393797835238961
= 43 * 10781 * 391441 * 428597443 * 11795628769 * 408944901028399 *
22566921596365593811470735460776534824496318810581339, where Q = 29 *
70326806362093 and R = 7Q.
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CROSSREFS
| Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A139775 A087528 A144839 * A023926 A022068 A198805
Adjacent sequences: A124989 A124990 A124991 * A124993 A124994 A124995
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KEYWORD
| more,nonn
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AUTHOR
| Nick Hobson Nov 18 2006
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